Generalized Diffusion Theory for Radiative Transfer in Fully Anisotropic Scattering Media

Year: 2026

Authors: Pini E., Giusfredi M., Pattelli L.

Autors Affiliation: Ist Nazl Ric Metrol INRiM, Turin, Italy; European Lab Nonlinear Spect LENS, Sesto Fiorentino, Italy; Univ Firenze, Dipartimento Fis & Astron, Sesto Fiorentino, Italy; CNR, Ist Sistemi Complessi, Sesto Fiorentino, Italy; Ist Nazl Fis Nucl, Sez Firenze, Sesto Fiorentino, Italy; CNR, Ist Nazl Ott, CNR INO, Sesto Fiorentino, Italy.

Abstract: A generalized anisotropic-diffusion framework is developed for transport problems in media described by a tensorial scattering coefficient and a scalar Henyey-Greenstein asymmetry factor. In this regime the classical similarity relation between scattering and transport parameters fails, and each principal diffusion coefficient depends on all components of the microscopic scattering rate. Explicit expressions are derived for the direction-averaged mean free path, the diagonal elements of the diffusion tensor, and boundary condition lengths via rapidly convergent spherical-harmonics expansions, along with open-source implementations. The resulting predictions are validated against anisotropic Monte Carlo simulations, showing excellent agreement across broad ranges of structural anisotropy and phase-function asymmetry factors. The theory provides a compact, general route connecting microscopic anisotropic scattering to macroscopic diffusion coefficients and boundary conditions in bounded geometries.

Journal/Review: ADVANCED THEORY AND SIMULATIONS

Volume: 9 (6)      Pages from: e70430-1  to: e70430-14

More Information: The authors thank Fabrizio Martelli, Andre Liemert and Alwin Kienle for fruitful discussion. This work was partially funded by the European Union’s NextGenerationEU Programme with the I-PHOQS Research Infrastructure (IR0000016, ID D2B8D520, CUP B53C22001750006) Integrated infrastructure initiative in Photonic and Quantum Sciences. L.P. acknowledges the CINECA award under the ISCRA initiative, for the availability of high performance computing resources and support (ISCRA-C ARTTESC2). Open access publishing facilitated by Istituto Nazionale di Ricerca Metrologica, as part of the Wiley-CRUI-CARE agreement.
KeyWords: anisotropic diffusion; monte carlo simulations; photon transport; radiative transfer; scattering media
DOI: 10.1002/adts.70430